be the orthogonal complement in \(\mathrm {H}^2\)  of the subspace of all those \(\mathrm {H}^2\)  functions that vanish at \(A_n\) . Observe that if \(A_n=z_n\)  is a \(1\times 1\)  scalar in \(\mathbb {D}\) , then \(H_n\)  is the line spanned by the Szegö kernel at \(z_n\) , thanks to the reproducing property in (REF ). With this in mind, one can extend the notion of Riesz and Bessel system to any sequence \((\mathcal {H}_n)_{n\in \mathbb {N}}\)  of closed subspaces of a Hilbert space \(\mathcal {H}\) , by asking that there exists a positive \(C\)  so that, for any sequence of unit vectors \((h_n)_{n\in \mathbb {N}}\)  chosen in \(\mathcal {H}\)  so that each \(h_n\)  belongs to \(\mathcal {H}_n\) , (REF ) holds (or, in the case of a Bessel system, the right inequality in (REF ) holds). Carleson's Theorem and Shapiro and Shields result in [1]} can be then extended to this matrix node interpolation problem as follows, [2]} [3]}:
